Substantially rigid plastic containers with replaceable covers, e.g., bucket-type containers, are commonly used to package and ship selected liquid materials in the nature of foods and food preparation materials, cosmetic preparations, detergents, and the like. Such containers are sturdy, typically having a wall thickness in the range of about 0.075 inch to about 0.090 inch, and have a large mouth that renders them well suited for storing and dispensing a variety of viscous liquids, e.g., syrups, mustard, and cosmetic preparations. Another mode of shipping liquid products is the “bag & box” arrangement in which a bag, made of flexible single or double ply plastic film and provided with a fitment for discharge of the bag's contents, is stored in a box made of corrugated cardboard. The latter type of packaging system is well suited for free-flowing liquids such as vinegar, wine, detergents, and the like. However, it is not well suited for viscous materials for a number of reasons. For example, it is difficult to remove all of the contents from the bag, due to the inability to scrape out the residual contents from the bag. Additionally, in the case of a material that consists of several ingredients that tend to separate from one another on standing, it is not possible to introduce a stirring implement into the bag for the purpose of mixing the contents to obtain a homogenous material. Further limitations stem from plastic recycling requirements and food packaging regulations. Environmental regulations require containers with a volume of 5gallons or less to be made of a recycleable material. Additionally governmental regulations require that plastic containers for foodstuffs be made of a virgin plastic material. The substantially rigid plastic containers comprise a relatively large amount of plastic in comparison to the flexible bags used in the “bag & box” packaging system, thereby increasing the amount of plastic that has to be disposed of or recycled. Making such containers of virgin plastic is costly and hence discourages their use for containing foodstuffs. The “bag & box” system employs less plastic, but the bags are not as sturdy as the substantially stiff containers and also cannot be used where it is essential to access all of the contents or where it is desired to mix the contents in situ.